Question on order of horizontal transformation

[Veena_desai]

Given f(x) = 1/3x^2+7

Perform the following operations;
1. Refecttion in the y axis
2. Horizontal stretch by a factor of 2
3. Horizontal translation 8 units right.



Perform the following operations;
1. Horizontal stretch by a factor of 2
2. Refecttion in the y axis
3. Horizontal translation 8 units right.


Perform the following operations;
1. Horizontal stretch by a factor of 2
2. Horizontal translation 8 units right.
3. Refecttion in the y axis


Perform the following operations;
1. Horizontal translation 8 units right.
2. Horizontal stretch by a factor of 2
3. Refecttion in the y axis

How do each of the above differ in the way the transformations are applied.

Appreciate if someone can help me understand.

thx,
Veena

 

[Harry_the_cat]

The order in which the tranformations are performed affects the result.

I would suggest you first sketch a graph of y = f(x) and physically do the transformations in the given order to see the different results.

 

[HallsofIvy]

Given f(x) = 1/3x^2+7

This is ambiguous. Probably it means (1/3)x^2+ 7 but it could mean 1/(3x^2)+ 7 or even 1/(3x^2+ 7). I will assume you mean (1/3)x^2+ 7.

Perform the following operations;
1. Reflection in the y axis

(x, y) becomes (-x, y)
f(x)= (1/3)(-x)^2+ 7= (1/3)x^2+ 7

2. Horizontal stretch by a factor of 2

(x, y) becomes (x/2, y)
f(x)= (1/3)(x/2)^2+ 7= (1/12)x^2+ 7

3. Horizontal translation 8 units right.

(x, y) becomes (x- 8, y)
f(x)= (1/12)(x- 8)^2+ 7= (1/12)x^2- (4/3)x+ (16/3)+ 7
= (1/12)x^2- (4/3)x+ 37/3


Perform the following operations;
1. Horizontal stretch by a factor of 2

(x, y) becomes (x/2, y)
f(x)= (x^2/4)/3+ 7=x^2/12+ 7

2. Reflection in the y axis

(x, y) becomes (-x, y)
f(x)= (-x)^2/12+ 7= x^2/12+ 7

3. Horizontal translation 8 units right.

(x, y) becomes (x- 8, y)
f(x)= (x- 8)^2/12+ 7= x^2/12- (4/3)x+ 16/3+ 7= x^2/12- (4/3)x+ 37/3.

Perform the following operations;
1. Horizontal stretch by a factor of 2

(x, y) becomes (x/2, y)
f(x)= (1/3)(x/2)^2+ 7= x^2/12+ 7

2. Horizontal translation 8 units right.

(x. y) becomes (x- 8, y)
f(x)= (x- 8)^2/12+ 7= x^2/12+ (4/3)x+ 16/3+ 7= x^2/12+ (4/3)x+ 37/3

3. Reflection in the y axis

(x, y) becomes (-x, y)
f(x)= (-x)^2/12+ (4/3)(-x)+ 37/3= x^2/12- (4/3)x+ 37/3

Perform the following operations;
1. Horizontal translation 8 units right.

(x, y) becomes (x- 8, y)
f(x)= (1/3)(x- 8)^2+ 7= (1/3)x^2- (16/3)x+ 64/3+ 7= (1/3)x^2- (16/3)x+ 85/3

2. Horizontal stretch by a factor of 2

(x, y) becomes (x/2, y)
f(x)= (1/3)(x/2)^2- (16/3)(x/2)+ 85/3= x^2/12- (8/3)x+ 85/3

3. Reflection in the y axis[/quote
(x, y) becomes (-x, y)
f(x)= (-x)^2/12- (8/3)(-x)+ 85/3= x^2/12+ (8/3)x+ 85/3

How do each of the above differ in the way the transformations are applied.

Appreciate if someone can help me understand.

thx,
Veena

 

[Veena_desai]

This is ambiguous. Probably it means (1/3)x^2+ 7 but it could mean 1/(3x^2)+ 7 or even 1/(3x^2+ 7). I will assume you mean (1/3)x^2+ 7.


(x, y) becomes (-x, y)
f(x)= (1/3)(-x)^2+ 7= (1/3)x^2+ 7

Thank you!
This clears all my questions